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Relationship B has a lesser rate than Relationship A. The graph represents Relationship A.

Which table could represent Relationship B?


First-quadrant graph showing a ray from the origin through the points (5, 2) and (10, 4).

Horizontal axis label is Time in weeks. Vertical axis label is Plant growth in inches.


A.

Time (weeks) 3 4 6 9

Plant growth (in.) 1.8 2.4 3.6 5.4



B.

Time (weeks) 3 4 6 9

Plant growth (in.) 0.9 1.2 1.8 2.7



C.

Time (weeks) 3 4 6 9

Plant growth (in.) 1.5 2 3 4.5



D.

Time (weeks) 3 4 6 9

Plant growth (in.) 2.7 3.6 5.4 8.1

Verified Answer :

Table B could represent Relationship B

 

Time (weeks) 3 4 6 9

Plant growth (in.) 0.9 1.2 1.8 2.7

 

The correct answer between all
the choices given is the second choice or letter B. I am hoping that this
answer has satisfied your query and it will be able to help you in your
endeavor, and if you would like, feel free to ask another question.

Answer:

The correct option is B.

Step-by-step explanation:

If a line passing through two points, then the slope of a line

\(m=\frac{y_2-y_1}{x_2-x_1}\)

It is given that the in Relationship A, the line passing through the points (5, 2) and (10, 4). Rate of change of Relationship A is,

\(m_A=\frac{4-2}{10-5}=\frac{2}{5}=0.4\)

In option A, the Rate of change of Relationship B is,

\(m_B=\frac{2.4-1.8}{4-3}=\frac{0.6}{1}=0.6\)

In option B, the Rate of change of Relationship B is,

\(m_B=\frac{1.2-0.9}{4-3}=\frac{0.3}{1}=0.3\)

In option C, the Rate of change of Relationship B is,

\(m_B=\frac{2-1.5}{4-3}=\frac{0.5}{1}=0.5\)

In option D, the Rate of change of Relationship B is,

\(m_B=\frac{3.6-2.7}{4-3}=\frac{0.9}{1}=0.9\)

Only in option B, the Relationship B has a lesser rate than Relationship A. Therefore option B is correct.

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